Have you considered a Ruger Single-Ten? It's admittedly a bit slow to reload, but it's also incredibly soft shooting and the fiber optic sights really pop on indoor ranges. Every time I pull back the hammer I think to myself "Mmmmm...buttery smooth."

There will be a SP101 in 22 mag next year. It will be sent in for testing to be on the roster.
Not sure on the price, 22 version was $580?
The discontinued S&W kit gun, the expensive 617-$800?
The Heritage revolvers have had good reviews for single actions.
Good Luck

Single actions are cowboy type and double action the cyl swings out. IMO double action would be the best first gun. They are easier to shoot due to the frame style. A quality 22 should last close to a life time no matter the choice.

And about that "no 6" barrel" limitation....IMHO you will enjoy it more if you hit more, and you will hit more with a longer barrel. I've taught all 3 of my wives (they weren't simultaneous, thankfully) and both my sons how to shoot, and they all started with Ruger Mk 1 or Mk IIs, despite my protests. Shows how much they listened to the old man!

The LCR looks good but I don't think it has been approved for CA yet so it may take awhile.

If Ruger submits the LCR-22 for roster approval, and if CA DOJ doesn't lag, then we might see it approved sooner than we think. They submitted the .357 LCR for roster approval and that was made available to CA residents fairly quickly.